Editing Dynamic nuclear polarization (section)

===Cross effect===

====Static case====
The cross effect requires two unpaired electrons as the source of high polarization. Without special condition, such a three spins system can only generate a solid effect type of polarization. However, when the resonance frequency of each electron is separated by the nuclear Larmor frequency, and when the two electrons are dipolar coupled, another mechanism occurs: the cross-effect. In that case, the DNP process is the result of irradiation of an allowed transition (called single quantum) as a result the strength of microwave irradiation is less demanded than that in the solid effect. In practice, the correct EPR frequency separation is accomplished through random orientation of paramagnetic species with g-anisotropy. Since the "frequency" distance between the two electrons should be equal to the Larmor frequency of the targeted nucleus, cross-effect can only occur if the inhomogeneously broadened EPR lineshape has a linewidth broader than the nuclear Larmor frequency. Therefore, as this linewidth is proportional to external magnetic field B<sub>0</sub>, the overall DNP efficiency (or the enhancement of nuclear polarization) scales as B<sub>0</sub><sup>−1</sup>. This remains true as long as the relaxation times remain constant. Usually going to higher field leads to longer nuclear relaxation times and this may partially compensate for the line broadening reduction.
In practice, in a glassy sample, the probability of having two dipolarly coupled electrons separated by the Larmor frequency is very scarce. Nonetheless, this mechanism is so efficient that it can be experimentally observed alone or in addition to the solid-effect.<ref name=":0" /><ref>{{Cite journal |last=Abragam |first=A |last2=Goldman |first2=M |date=1978-03-01 |title=Principles of dynamic nuclear polarisation |url=http://dx.doi.org/10.1088/0034-4885/41/3/002 |journal=Reports on Progress in Physics |volume=41 |issue=3 |pages=395–467 |doi=10.1088/0034-4885/41/3/002 |issn=0034-4885|url-access=subscription }}</ref>

====Magic angle spinning case====
As in the static case, the MAS-DNP mechanism of cross effect is deeply modified due to the time dependent [[energy level]]. By taking a simple three spin system, it has been demonstrated that the cross-effect mechanism is different in the Static and MAS case. The cross effect is the result of very fast multi-step process involving EPR single quantum transition, electron dipolar anti-crossing and cross effect degeneracy conditions.
In the most simple case the MAS-DNP mechanism can be explained by the combination of a single quantum transition followed by the cross-effect degeneracy condition, or by the electron-dipolar anti-crossing followed by the cross-effect degeneracy condition.<ref name="Mentink-Vigier, F. Akbey, U. Hovav, Y. Vega, S. Oschkinat, H. Feintuch, A. 2012 13–21"/><ref name=tycko12>
{{cite journal
|author =Thurber, K. R. |author2=Tycko, R.
|title = Theory for cross effect dynamic nuclear polarization under magic-angle spinning in solid state nuclear magnetic resonance: the importance of level crossings
|journal = [[J. Chem. Phys.]]
|volume = 137 |pages = 084508
|year = 2012
|doi = 10.1063/1.4747449
|pmid=22938251
|issue = 8 |bibcode = 2012JChPh.137h4508T
|pmc = 3443114}}</ref>

This in turn change dramatically the CE dependence over the static magnetic field which does not scale like B<sub>0</sub><sup>−1</sup> and makes it much more efficient than the solid effect.<ref name=tycko12 />